To render the color of the stars fairly well, I’d use daylight so as to balance the range of color evenly between red and blue. However, the color of the night sky can be problematic: what looks sky blue to me will often turn out orange due to urban street lighting.
Be aware that in dim lighting the eye’s own color perception is strongly altered due to the Purkinje Effect, which lessens the eye’s response to long wavelengths of light. Because of this, what the camera captures is likely not what you see, which is why the color of city lighting can appear to be much more prominent in photos compared to human vision.
Because of the Purkinje Effect, I’d adjust the colors to be closer to how I remember seeing them, and that is typically a dark sky blue color, which is biased from blue towards cyan, and not from blue towards purple. Adjust so that B > G > R in the image. If this shifts the color of the stars too much, you can always use a mask to not modify the color of the stars.
I developed a Photoshop action that will largely correct for the Purkinje Effect, but unfortunately it is specific to my particular model of camera.
Typically I try to underexpose the image enough so that the stars keep most of their color, and then bring up the sky brightness and color in post processing.